ln(2)+ln(x)=ln(8)+ln(2x-3)

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Solution for ln(2)+ln(x)=ln(8)+ln(2x-3) equation:


Simplifying
ln(2) + ln(x) = ln(8) + ln(2x + -3)

Reorder the terms for easier multiplication:
2ln + ln(x) = ln(8) + ln(2x + -3)

Multiply ln * x
2ln + lnx = ln(8) + ln(2x + -3)

Reorder the terms for easier multiplication:
2ln + lnx = 8ln + ln(2x + -3)

Reorder the terms:
2ln + lnx = 8ln + ln(-3 + 2x)
2ln + lnx = 8ln + (-3 * ln + 2x * ln)
2ln + lnx = 8ln + (-3ln + 2lnx)

Combine like terms: 8ln + -3ln = 5ln
2ln + lnx = 5ln + 2lnx

Solving
2ln + lnx = 5ln + 2lnx

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '-5ln' to each side of the equation.
2ln + -5ln + lnx = 5ln + -5ln + 2lnx

Combine like terms: 2ln + -5ln = -3ln
-3ln + lnx = 5ln + -5ln + 2lnx

Combine like terms: 5ln + -5ln = 0
-3ln + lnx = 0 + 2lnx
-3ln + lnx = 2lnx

Add '-2lnx' to each side of the equation.
-3ln + lnx + -2lnx = 2lnx + -2lnx

Combine like terms: lnx + -2lnx = -1lnx
-3ln + -1lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-3ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(3 + x) = 0

Ignore the factor -1.

Subproblem 1

Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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